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The main problems and the approach used by the authors for roughness metrology of super-smooth surfaces designed for diffraction-quality X-ray mirrors are discussed. The limitations of white light interferometry and the adequacy of the method of atomic force microscopy for surface roughness measurements in a wide range of spatial frequencies are shown and the results of the studies of the effect of etching by argon and xenon ions on the surface roughness of fused quartz and optical ceramics, Zerodur, ULE and Sitall, are given. Substrates of fused quartz and ULE with the roughness, satisfying the requirements of diffraction-quality optics intended for working in the spectral range below 10 nm, are made.
© 2014 Optical Society of America
1. Introduction
In connection with the progress in the technology of the deposition of normal incidence multilayer mirrors [1,2], there is now a real possibility of transferring conventional optical methods to extreme ultraviolet (EUV) and soft X-ray (SXR) ranges. Among the most important optics applications actively discussed in recent years are nanolithography at a wavelength of 13.5 nm, as well as beyond extreme ultraviolet (BEUV) lithography at 6.7 nm [3,4]. Very promising is the X-ray microscopy of biological objects in the areas of “water” and “carbon” transparency windows, at 2.3–5 nm wavelengths [5,6]. To ensure diffraction-quality imaging, when the spatial resolution is determined only by the radiation wavelength and the numerical aperture of the lens, substrates with atomically smooth surfaces are required.
With the impact on the image, the roughness is divided into low frequency at a lateral dimension range of 1 mm – 1 m, middle frequency at 1 µm – 1 mm and high frequency at 1 nm – 1 μm [7]. High-frequency roughness leads to radiation scattering at angles greater than the width of the Bragg reflection peak of the multilayer mirror and to a sharp loss in reflectivity of the mirrors. Since interference gain of scattered waves does not occur, the contrast of the image is not affected, leading only to a loss of light. Roughness in the low-frequency range, with lateral dimensions in the range of 1 mm – 1 m, does not affect the luminance and contrast of the image, and leads to a distortion of the image as a whole. For example, rings are shown as ellipses.
The greatest effect on the spatial resolution of the mirror is roughness of the middle-frequency range. For EUV lithography at 13.5 nm, the root mean-square (r.m.s.) roughness should not exceed σ ≤ 0.2 nm [8–10]. The scaling factor at the transition to the other wavelength λ can be written as (σ/λ)2 [11]. Accordingly, reducing the operating wavelength requires at least a proportional decrease in the roughness. For example, for a wavelength shorter than 6 nm the roughness should not exceed 0.1 nm.
Solving the problem of manufacturing super-smooth optical surfaces involves two main tasks. The first is an audit of the capabilities of the traditional and the development of new methods for roughness measurements with sub-angstrom sensitivity. The second is improving the traditional and developing new methods of polishing. It is clear that the solution to the problem of manufacturing super-smooth low-scattering substrates is of interest not only for EUV and SXR, but also for other optical ranges.
In this paper, we report on the latest results of the research undertaken by the authors into manufacturing substrates satisfying the requirements for diffraction-quality optics in the spectral range shorter than 10 nm. Two main aspects of the problem of creating substrates are considered: the first is related to the development of adequate methods for measuring the roughness and the second is the development of advanced polishing methods. With respect to metrology, we propose an approach in which reliable data are only those that are confirmed by the “first-principle” method of diffuse X-ray scattering (DXRS) [12–15]. To improve the process of obtaining super-smooth substrates for multilayer mirrors, we studied the impact of ion-beam etching on the surface roughness of fused silica and optical ceramics: Zerodur, ULE and Sitall, which have abnormally low coefficients of thermal expansion and, therefore, are of greatest interest for ultra-high spatial resolution systems.
2. Roughness measurement
Traditionally, for roughness measurements, atomic force microscopy (AFM) and white light interferometry (WLI) [16,17] have been used. In a number of papers, good agreement between AFM and WLI measurement results [7,9,18,19] is observed. In some papers, in contrast, the contradictory nature of the WLI data is marked. In [20,21] the problems which arise when these methods are applied to the study of super-smooth optical surfaces and the principal causes of these contradictions are analysed. In particular, both AFM and WLI cannot be attributed to the “first-principle” methods. For example, the results of AFM measurements are strongly affected by the geometric dimensions of the probe, the surface under study, electrification and contamination, and the non-linearity of the piezo-scanner, which is most pronounced on “large” frames [22]. Another source of uncertainty in AFM measurements is sample homogeneity and the fact that only a very small sample area is investigated (ergodic hypothesis).
In the WLI method, the surface profile is measured directly due to the interference of light reflected from the surface under study and a reference. Since the coherence length in WLI is small, the maximum contrast of the interference pattern is achieved with strict equality of the optical paths. Alignment of the paths occurs due to displacement of the lens mounted on a piezo-ceramic. An obvious source of error in this method is the non-linearity of the piezo-electric ceramic and/or the capacitor position sensor, if present, which means that both the inclination of the sample with respect to the reference and the surface profile of the measurement results are influenced. The other error sources are the roughness of the reference surface and the errors that occur when light passes through the optical elements. The importance of the latter was demonstrated by interferometry with a diffraction reference wave which was used to study the shape of the surfaces and the aberrations of the optical systems [23,24]. Therefore, it is essential for this type of instrument to have a so-called transfer function of the optical path using a “mythical” reference.
Therefore, in practice, the adequacy of the AFM and WLI must be confirmed by the “first-principle” method, as it was, for instance, in the case of point diffraction interferometry, used for precision measurements of low frequency roughness, and when aberrations of the reference wave were measured in a simple Young’s experiment on two-source interference [25,26]. Moreover, taking into account variable external factors, for example, the samples under study having very different reliefs, slopes with respect to the reference, mechanical vibration, and so on, such inspections must be carried out regularly. Ideally, for each surface the measurements obtained using different methods should be compared.
Since the physics of scattering X-ray radiation by the rough surfaces is well known, the diffuse scattering of X-rays is the most reliable “first-principle” method for roughness measurements [12–15].
In our work we apply an approach based on the perturbation theory (for details, see [27]), which makes possible to recover the power spectral density (PSD) function of the surface directly from the experimental data without a priori assumptions concerning its topography. This is possible due to a linear relationship between the scattering indicatrix and the PSD function. For example, if radiation with the wavelength λ falls at grazing angle θ0, see Fig. 1(a), on a surface with correlation length a, the widths of the scattering indicatrix Φ(θ,ϕ) in perpendicular directions θ and ϕ can be estimated as δθ ~λ/παsinθ0 and δϕ ~λ/πα. For X-ray radiation and grazing incidence, for isotropic or weakly anisotropic surfaces, this means that δϕ << δθ, since θ0 << 1. In practice [18,27] the angular dimension Δϕ of the X-ray detector far exceeds δϕ in the azimuthal direction; that is, integration of the scattered signal over the slit of the detector is identical to the measurement of the one-dimensional indicatrix
which is related to the one-dimensional PSD1D function as [15]where ε is the permittivity of the medium, ν is the spatial frequency of the roughness, andis the Fresnel transmission coefficient. The roughness values σ are calculated in accordance with the expression:where νmin and νmax, the minimal and the maximal spatial frequencies.
Fig. 1 Diffusion scattering of X-ray radiation: geometry – (a) and a typical one-dimensional indicatrix taken at λ = 13.5 nm – (c).
The X-ray diffusion scattering experiment geometry and a typical one-dimensional indicatrix taken at λ = 13.5 nm are given in Fig. 1. Due to the grazing incidence a typical probe X-ray beam spot on a sample under study is about 2 × 10 mm2 in the case of λ = 13.5 nm and 10 × 15 mm2 when λ = 0.154 nm that provides good averaging over entire roughness frequency region and substrate area.
PSD functions of the roughness for different fused silica substrates obtained by means of AFM, WLI and DXRS at the wavelength of 0.154 nm are presented in Fig. 2(a)-2(c). The effective roughness σeff is achieved as a result of the integration of the AFM and DXRS data in the range of spatial frequencies 10-2 – 102 µm−1.
Fig. 2 PSDs for fused silica substrates polished with different technologies as obtained by WLI, DXRS and AFM – (a-c).
The figure shows that, for the substrate with an effective roughness σeff = 1.40 nm, the PSD function obtained by WLI agrees well with the AFM and DXRS data, up to the maximum operating frequency corresponding to a lateral size of about 3 μm. However, for the substrate with σeff = 0.42 nm, the measurement data can be considered as adequate only for roughness with a lateral size greater than 30 μm. For shorter-wavelength roughness there is a strong discrepancy between the results of the measurements of WLI, AFM and DXRS. For the substrate with σeff = 0.24 nm, coincidence of the WLI measurements with AFM and DXRS can be expected since the lateral size is about 160 μm, if one approximates the curve of the diffuse scattering in this area
It should be noted that, independently of effective roughness of the investigated substrates, DXRS and AFM data coincide well with each other. Thus, these data indicate that the WLI method does not provide reliable measurements when applied to ultra-smooth surfaces. This conclusion relates generally to the method and not to a specific device, as cross-tests were made on four different devices from two WLI manufacturers, see for example [21,28].
As can be seen from these figures, when studying the weakly scattering (super-smooth) surfaces, the standard DXRS technique at a wavelength of 0.154 nm has a short-wavelength border of about 1 μm−1. Thus, strictly speaking, the high spatial frequencies also require validation of the AFM measurements by the “first-principle” method. To solve this problem, we developed a special reflectometer with an operating wavelength of 13.5 nm. The greater scattering ability of the matter in the SXR range allows one to extend the working range to the higher frequencies. With a high-aperture monochromator and a powerful X-ray tube, and undertaking the experiment in a vacuum (no scattering in the air as compared with the conventional experiments on DXRS at the 0.154 nm wavelength) using an efficient single-photon X-ray detector (quantum efficiency at a wavelength of 13.5 nm is near unity) the angular dependencies of the diffuse scattering intensity, with a dynamic range of up to eight orders of magnitude, see Fig. 1(b), were measured. The PSD function obtained at this wavelength is shown in Fig. 3 by the line with hollow circles. As one can see from the figure the shapes of the PSD curves repeat each other well. The difference in the effective roughness of about 30% we attribute to the inaccuracy of the optical constants of silicon near the L-absorption edge, λ = 12.4 nm, taken from [29], and to errors in the experimental geometry. Additional scattering may occur due to sub-surface volumetric inhomogeneities, which we did not investigate carefully in this experiment. However, if it is necessary it can be done by the method described in [21].
Thus, the “first-principle” method of DXRS confirmed the adequacy of the AFM in the 10−2–102 μm−1 range of spatial frequencies of roughness, thus it became possible to control (eliminate) the influence of factors other than surface roughness on the AFM measurements.
Another source of measurement error, which is most pronounced in the study of super-smooth substrates, is the inherent AFM noise. The sources of noise are mechanical vibrations, the thermal fluctuations of the probe and the noise of the electronics. The PSD function of the noise was determined in the following manner. The probe was brought to the surface and fake scans, with typical frames of 2 × 2 and 40 × 40 μm, were carried out using a stationary probe. The restored curve of noise power spectral density is shown in Fig. 4. Since the noise, characterized by σnois, and the surface roughness, σsub, are statistically independent random variables, the effective (measured experimentally) roughness σeff, can be written as the sum of the squares of the surface roughness and noise. In this case, to recover the PSD of the surface roughness, the following formula can be used
The formula shows that the PSD functions of roughness and noise are additive. As follows from the figure, the effective AFM noise in the 2 × 2 μm frame was 0.065 nm, and in the 40 × 40 μm frame was 0.077 nm. Over the entire range of spatial frequencies where studies were conducted, the AFM noise σnois = 0.11 nm. Subsequently, where necessary, the formula will be used to determine the numerical value of the roughness.Thus, in practice, when studying the roughness of super-smooth substrates, we adhere to the following rules. First, we do not use the WLI data and estimate the roughness with lateral dimensions in the range of 100 μm-1 mm by extrapolation of DXRS data. Second, regularly, and in important cases, such as developing of a new polishing method, we compare the measurement results of DXRS and AFM. Third, in the presence of discrepancies between AFM and DXRS data, we study the presence of disturbed sub-surface layer.
3. Sample preparation
The experiments were performed with substrates of two domestic grades of fused silica, QV and QU-1, in visible and ultraviolet ranges, respectively, and the Suprasil brand, as well as Zerodur, ULE and domestic analogue Sitall optical ceramics. Samples were prepared by the deep grinding-polishing method, whereby in each subsequent processing step material to a depth equal to two dimensions of the abrasive grains applied in the previous step is removed. The machining of most samples was finished using a polishing suspension with an abrasive grain size of 0.8–1 μm. Record results, discussed below, were obtained when the mechanical polishing was finished with a polishing oxide nominal grain size of 0.2–0.3 μm. The finishing was the standard for chemical-mechanical polishing in the micro-electronics industry.
Thus, prepared samples were subjected to ion-beam etching. This study had three objectives. First, to check a large set of experimental data of various authors, using improved methods to study the roughness; second, to verify the stability of the materials for ion-beam etching, as this process is often used at the precision shape correction stage (local correction, aspherization) of the substrate surfaces for ultra-high spatial resolution systems; and, third, to search for the conditions under which the surfaces can be smoothed. Along with the determination of optimal ion energy, we were interested in the influence of the depth of the material removed on the surface roughness over a wide range, as, if the local error correction removal ranges from a few to hundreds of nanometres, the removal, during aspherization, can reach tens of micrometres. Etching was carried out only at normal angles of incidence of the ions to the surface to be treated for two reasons: first, at near normal angles of incidence, the smallest roughness development was observed [30,31], and second, normal incidence provides a constant etching rate and size of ion beam on the surface, prerequisites for the precise local shape correction of the substrates.
Etching was carried out using a miniature and two wide-aperture ion-beam sources. The energy of the ions can be smoothly varied from 100 to 1000 eV. The processed sample was mounted on a five-axis goniometer. The goniometer provides installation the local normal to the surface along the beam axis at any point of the sample. Samples can be of any surface shape with a numerical aperture of up to NA = 0.5 and a diameter of up to 300 mm. Ion sources are equipped with a charge compensator that can handle both conductive and dielectric materials [32].
4. Experimental results for fused silica
The results of etching by argon ions with different energies are illustrated in Fig. 5, which shows the PSD function of roughness before and after etching. Figure 5(a) corresponds to the ion energy of 200 eV, Fig. 5(b) - 400 eV, Fig. 5(c) - 600 eV and Fig. 5(d) - 1000 eV. The material removal was about 300 nm. As can be seen from the figure, a noticeable smoothing of the surface is observed at the energy level of about 1000 eV. Effective roughness decreased from 0.44 to 0.33 nm. The smoothing occurs mainly in the high-frequency region, since the roughness lateral size of 3 μm. Such behaviour is observed when removing material from 200 nm to 10 μm.
Fig. 5 PSD functions of roughness of fused silica substrates before and after etching with argon ions at energies of a) - 200, b) - 400, c) - 600 and d) - 1000 eV. Etching depth was approximately the same and was about 300 nm.
Since middle-range roughness is the greatest for diffraction-quality optics, then etching with argon is not enough to solve the problem of creating substrates for diffraction-quality optics with short-wave borders beyond 10 nm. Therefore, etching with xenon ions was studied. The reasons for using xenon were as follows. First, compared with argon, the mass of xenon is three-fold higher. This leads to the xenon ions interacting more effectively with the lattice, rather than with single atoms, and transferring energy in their excitation. This excitation can be transferred by the phonon mechanism to the least bound surface atom while it is far from the point of interaction. Thus, one can expect an effect on the roughness with larger lateral dimensions. Second, the lower penetration depth of the ions (atoms) also increases the efficiency of the interaction with the surface.
Figure 6 shows the spectral power density of the roughness of fused quartz substrates before and after etching by xenon ions. The effective roughness of the samples before etching was 0.46 nm. Etching was performed at ion energy of 200, 400, 600 and 800 eV. The etching depth was approximately the same and was about 300 nm. The figure shows that the greatest smoothing of the surface is achieved at ion energy of 600 eV. The effective roughness fell by almost two angstrom and was 0.27 nm. The smoothing, as expected, starts with the roughness with a lateral dimension of 10 μm, thus managing to significantly reduce the middle-frequency roughness.
Fig. 6 PSD functions of roughness of fused silica substrates before and after etching with xenon ions at energies of a) - 200, b) - 400, c) - 600 and d) - 800 eV. Etching depth was approximately the same and was about 300 nm.
To demonstrate the potential of the smoothing, substrates with original effective roughness of 0.22 and 0.32 nm (mechanical polishing finished with grain sizes of 0.2–0.3 μm in suspension) were etched by xenon ions with energy of 600 eV. Figure 7 shows the results of the experiment. As in the previous case, the positive effect on roughness begins at lower frequencies corresponding to the lateral size of 10 μm. The measured effective roughness, see Fig. 7(b), decreased from 0.22 to 0.17 nm. If we consider AFM noise, then, according to Eq. (5), the effective roughness is a record 0.135 nm, and is in a frame 2 × 2 μm – 0.03 nm.
Fig. 7 PSD functions of roughness of fused silica substrates before (polishing was finished with a suspension grain size of 0.2–0.3 μm) and after etching by xenon ions with an energy of 600 eV.
Changing of the topography and the surface profile after etching by Xe ions with the energy of 600 eV is shown in Fig. 8. Figure 8(a) corresponds to the as-prepared sample and Fig. 8(b) – to the sample after etching.
Fig. 8 AFM topography and surface profile of fused silica substrate: a) – as- prepared and b) - after etching by xenon ions with an energy of 600 eV.
Thus, the application in the final stage of etching by xenon ions with energy of 600 eV noticeably improves the surface quality of the fused silica and meets the requirements of diffraction-quality optics for the spectral range beyond 10 nm.
5. Experimental results for optical ceramics
One of the most important requirements of the materials for mirrors is their dimensional stability, primarily over a wide range of temperatures. For example, when working in space or in a high volume manufacturing EUV lithographer, temperature fields on the surfaces of the mirrors have strong gradients. To ensure the thermal stability of the optical circuit at the desired level, optical ceramics with temperature coefficients lying in the range of 10−8 K−1, such as ULE, Zerodur and domestic analogue Sitall, are used. An additional requirement of these materials is the resistance of the surface roughness to processing by ion beams, which are widely used, for example, for correcting the surface shape.
In the present study, the roughness and resistance to etching by argon ions for these materials were compared. Polishing of Zerodur and Sitall was undertaken in a single cycle and ended with an abrasive grain size of 0.8–1 μm. At the final ULE polishing stage, the 0.2–0.3 μm abrasive grain size was used. Etching was undertaken using argon ions with energies of 300 and 800 eV. Figure 9 shows the results of the measurements of surface roughness before and after etching the samples of: Fig. 9(a) - ULE, Fig. 9(b) - Zerodur and Fig. 9(c) - Sitall. As can be seen from the figure, the original effective roughness of ULE was less than that of the other materials and was about 0.28 nm, while for Sitall and Zerodur it was about 0.42 nm. Based on our experience with fused silica, we believe that the main reason for this difference is the finer abrasive polishing.
Fig. 9 PSD functions of roughness: a) - ULE, b) - Zerodur and c) - Sitall. ULE: Etching # 1, ion energy of 300 eV, etch depth 1 μm; Etching # 2, ion energy of 800 eV, etch depth 1 μm; Etching # 3, ion energy of 800 eV, etch depth 3 μm. Zerodur: Etching # 1, ion energy 300 eV, etch depth 1 μm; Etching # 2, ion energy of 300 eV, etch depth 2 μm. Sitall: Etching # 1, ion energy of 300 eV, etch depth 1 μm; Etching # 2, ion energy of 300 eV, etch depth 3 μm.
The dynamics of the roughness during etching with argon ions is interesting, Fig. 9. When etching Sitall to a depth of about 1 μm, a noticeable decrease in the roughness is observed. Etching to a depth of 3 μm increase in the roughness in the high spatial frequencies follows.
At the same time, etching Zerodur leads to a significant increase in surface roughness even when removing material to a depth of 1 μm. Evaluation of the surface topography after etching by Ar ions with the energy of 300 eV for this sample is shown in Fig. 10. Figure 10(a) corresponds to the as-prepared sample and Fig. 10(b) – to the sample after etching. The figure demonstrates strong degradation of the surface.
Fig. 10 AFM surface topography of Zerodur substrate: a) – as prepared and b) - after etching by argon ions with energy of 300 eV at the removal depth of 1 μm.
The best behaviour during ion-beam etching demonstrates ULE. As seen in Fig. 9(a), at ion energies of 300 and 800 eV and etching to a depth of 3 μm, first smoothing and then stabilization of the roughness are observed. Such behaviour was observed experimentally during etching to a depth of 10 μm. It should be noted that during etching the measured effective roughness decreased from 0.28 to 0.18 nm. Considering the AFM noise, this corresponds to an effective surface roughness in the spatial frequency range of 10−2–102 μm−1 of 0.14 nm, which almost coincides with the best results obtained for fused silica.
6. Conclusions
In the example of fused silica substrates with different surface roughness, using the “first-principle” method of DXRS with the wavelengths of 0.154 and 13.5 nm, the limitation of WLI is demonstrated when it is applied for roughness measurements of super-smooth substrates. It is shown that it is necessary to consider the intrinsic noise of the AFM at the already achieved level of super-polishing for precision measurements of the roughness.
The positive effect on the surface roughness of fused silica of etching by xenon ions, both in middle- and high- frequency ranges, is shown. Optimal ion energy is about 600 eV. Additional “ion polishing” reduces the effective roughness in the range of spatial frequencies 0.025–60 μm−1 by about 1.5 angstrom, meeting the requirements of diffraction-quality optics for the spectral range beyond 10 nm. Smoothing of the surface is also observed under etching with argon ions. However, this effect becomes noticeable for smoothing roughness with spatial frequencies of 0.1–10 μm−1 at ion energy of about 1000 eV.
It is shown that the use of ion-beam etching for deep aspherization is purposeful for samples of fused quartz and ULE. By etching to a depth of 1–2 μm Sitall has similar characteristics. The worst results were for Zerodur, which showed a dramatic growth in roughness during etching, even in the case of relatively small, about 1 μm, etching depths. Thus Sitall and Zerodur can be etched to small depths sufficient only for precision local shape correction.
Thus, the advanced polishing processes, including ion-beam etching, of fused silica, Sitall, Zerodur and ULE satisfy the requirements of diffraction-quality optics for the spectral range beyond 10 nm. However we believe that, for applications with significant thermal loads and when “deep” ion-beam figuring of the mirrors is required, ULE is the most promising material for diffraction-quality X-ray optics.
Acknowledgments
This work was supported by Russian fund for basic researches, grants 14-02-00549, 13-02-97098 and 13-02-97045, by the Ministry of Science and Education of Russia as part of the programme of Public Centre of Using “Physics and technology of micro-and nanostructures” at Institute for physics of microstructures of the Russian academy of sciences.
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